A) \[\sqrt{\frac{2}{3}}\]
B) \[\sqrt{\frac{3}{2}}\]
C) \[\frac{3}{\sqrt{2}}\]
D) \[\frac{2}{3}\]
Correct Answer: A
Solution :
The length of perpendicular drawn from the vertex\[A(2,-1)\]to the base\[x+y=2\]is \[p=\left| \frac{2+(-1)-2}{\sqrt{{{1}^{2}}+{{1}^{2}}}} \right|\] \[=\left| -\frac{1}{\sqrt{2}} \right|=\frac{1}{\sqrt{2}}\] Let length of the side is a. In \[\Delta ABM,,\frac{p}{a}=\sin 60{}^\circ \] \[\Rightarrow \] \[a=\frac{p}{\sin 60{}^\circ }\] \[\Rightarrow \] \[a=\frac{\frac{1}{\sqrt{2}}}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{2}\sqrt{3}}\] \[\Rightarrow \] \[a=\sqrt{\frac{2}{3}}\]You need to login to perform this action.
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